The weights of an object are measured in a coal mine of depth ' $h_1$ ', then at sea level of height '…

The weights of an object are measured in a coal mine of depth ' $h_1$ ', then at sea level of height ' $\mathrm{h}_2$ ' and lastly at the top of a mountain of height ' $h_3$ ' as $W_1, W_2$ and $W_3$ respectively. Which one of the following relation is correct? [ $h_1 \ll R, h_3 \gg h_2=R, R=$ radius of the earth]
  1. $\mathrm{W}_1=\mathrm{W}_2=\mathrm{W}_3$
  2. $\mathrm{W}_1 \lt \mathrm{W}_2 \lt \mathrm{W}_3$
  3. $\mathrm{W}_1 \gt \mathrm{W}_2 \lt \mathrm{W}_3$
  4. $\quad \mathrm{W}_1 \lt \mathrm{W}_2\gt\mathrm{W}_3$

Solution

$\begin{aligned} & \text {Weight }=\mathrm{mg} \\ & \text {Value of ' } \mathrm{g} \text { ' is maximum on the surface of } \\ & \text {earth. As we go above or below the surface of } \\ & \text { earth, value of ' } g \text { ' decreases } \\ & \mathrm{W}_2\gt\mathrm{W}_1 \text { and } W_2 \gt W_3 \\ & \text { or } W_1 \lt W_2 \gt W_3\end{aligned}$ .

Asked in: MHT CET 2024 (15 May Shift 1)

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